How to generate Reaction Diffusion animation?
Since this site is meant to be as knowledge base … here is one option for Compositor. This technique mimics one used by image editor apps:

Copy - Blur - Subtract - Contrast - Merge - Save … repeat with saved image



Add any your black&amp;white image named like 0000.png from separate directory, because running rendering will generate an image sequence to that place.
The trick here is to reuse rendered and saved image for calculation of next frame. For that you have to add Texture node type Image Sequence even you have only your image for frame zero.
Offset -1  ... Thanks to @Robin Betts for pointing that.
To speed up animation you can close nodes into a Group and use it a few times in line.


Additional post-pro (generated sequence with Filter node type Sobel, regenerated and used with Displays modifier).


There is also option use Tissue addon for 3D object … version bundled with official Blender release doesn’t contain Cache feature, to get animated version get latest version from GitHub